аЯрЁБс;ўџ ўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRџџџџџџџџ РF€jю)бЇУ€2CompObjџџџџџџџџџџџџ\WordDocumentџџџџ<џџџџ .ObjectPool€рЅаАПw>бАПi§џџџўџџџўџџџўџџџ ўџџџ g(fџџџџ e!#џџџџ$%)џџџџC5*+.џџџџB/03џџџџ4 6789:;<=>?@A 2-џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ'dhџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџџџўџџџўџџџ ўџџџўџџџўџџџўџџџўџџџўџџџ !"#$%&'()*+,-./0ўџџџ2ўџџџўџџџ5ўџџџўџџџ8ўџџџ:;<=>?@ABCDEFGHIJўџџџLўџџџўџџџOўџџџўџџџRўџџџTUVWXYZ[\]^_`abўџџџdўџџџўџџџgўџџџўџџџjўџџџlmnopqrstuvwxyzўџџџ|ўџџџўџџџўџџџўџџџџџ РFMicrosoft Word 6.0 DocumentўџџџNB6WWord.Document.6;џў аЯрЁБс;џў Lўˆ,шшаЯрЁБс;џў Z:ЁdЗxpr  Œ :": ОЁР currentpoint  П" О,Times .џ+ H +0 ( :, Symbol)m) =) m +0ЁРSummaryInformation (џџџџџџџџџџџџџџџўўџџџС% Equation Native)*+,-./0џџџџџџџџџџџџ5џџўџџџџў8ўџџџ•/@_908716601FGHIJџџўџLџџўџџџўџOџџўџџџџџџџџџџџџџРFw>бАПw>бАП^_`Oleўџdџџўџџџўџgџџўџџџўџjџџўџlmnopџџџџџџџџџџџџuvwxy–џџџўP/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1856 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (H) 9 261 sh 224 /Times-Roman f1 (0) 287 357 sh (0) 1642 357 sh 384 /Times-Roman f1 (:) 522 261 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (m) 726 261 sh (m) 1410 261 sh 384 /Symbol f1 (=) 1075 261 sh end MTsave restore  ПЁd=MATH15 ƒH ˆ0 ‚:„m†=„m ˆ0 џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџўџџџ‚ўџџџ„…†‡ˆ‰Š‹ŒŽ‘ўџџџ“ўџџџўџџџўџџџўџџџ˜ўџџџš›œžŸ ЁЂЃЄЅІЇЈўџџџЊўџџџўџџџўџџџўџџџЏўџџџБВГДЕЖЗИЙКЛМўџџџОўџџџўџџџўџџџТУФХЦЧШЩўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў 1 ƒH ˆ0 ‚:„m†=„m ˆ0аЯрЁБс;џў аЯрЁБс;џў Lлt,шшаЯрЁБс;џў Z9ЁdЗxpr  Œ 9"9 ОЁРvгђЬч@^ЅбЇУ@Microsoft Word 6.0.14аЯрЁБс;џџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ  ˆ2аЯрЁБсўџ ђŸ…рOљhЋ‘+'Гй0ѕ˜я8Xx ~ Š –ЂЊ ВОл уэ90A84D8EA4428DA1368C9C2BOMacintosh HD:Applications:MS Word etc:Microsoft ofc:ms word 6:Templates:NormalA1. a) Using the axes below draw a box plot to represent the dataUniversity of WisconsinUniversity of Wisconsin'@ИБАП@€iversity of WisconsinаЯрЁБс;џў џџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџмЅhSР $eЎ.ѓ&ж&жж&ж&ж&ж&ж&€'@'@€'€'€'' '(€'ъ,[Ш'”\("~(~(~(‚(‚(‚(u+w+w+w+w+w+w+&E-X-‚+Mж&‚( ~(‚(‚(‚(+‚(ж&ж&~(Ш'‚(‚(‚(‚(ж&~(ж&~(u+ъ& '6ж&ж&ж&ж&‚(u+‚(ѓ‚(Sample Test 2 for Stat. 224 1. a) Using the following 10 random digit pairs, simulate 10 values of the discrete random variable X with probability density function X = 0 1 2 3 prob. = .12 .12 .60 .16 Random Digits 1 6 8 7 1 6 5 5 4 9 6 0 1 4 1 9 9 2 5 2 How many 2's in your list of simulated values? _______ b) Three independent normal random variables X,Y,Z have respective mean and standard deviation as follows random standard variable mean deviation X 2.0 0.8 Y 1.2 0.2 Z 1.6 0.4 Find (i) E(3X - 2Y + Z) (ii) Var(3X - 2Y + Z) What distribution does the random variable 3X - 2Y + Z have? 2. a) A pair of continuous random variables X,Y have the joint probability density function f(x,y) = 3/4 (x+y) on the triangular region sketched below, = 0 elsewhere. Fill in the marginal p.d.f. for X f(x) = 0 x < 0 or x > 1 = ___________ 0 < x < 1 b) The probability that a standard normal random variable Z lies between a and -a is .8664. Find a. 3. a) The manufacturer of a new fiberglass tire claims that they will last longer than the old tires which had an average life of 40,000 miles. To check this claim, a sample of 12 tires is tested with their lifetimes (in 1000еs of miles) being as follows Tire 1 2 3 4 5 6 7 8 9 10 11 12 Life 38.1 40.2 42.8 36.5 42 39.8 42 41 44.8 37.2 43 41 Test the manufacturerеs claim at the 5% significance level. b) The P-value for the hypothesis test  EMBED Equation.2  versus  EMBED Equation.2  turned out to be .416. (i) Would you reject the null hypothesis at the the 5% significance level? YES NO (Circle one) (ii) If the alternative hypothesis was  EMBED Equation.2  and the exact same sample data were obtained, what would the P-value be now? _________ (iii) If you were trying to persuade your boss that the alternative hypothesis was true, would you prefer a large or small P-value? (Circle one) 4. a) There are two different choices of a catalyst to stimulate a chemical process.To test whether the variance of the yield is the same no matter which catalyst is used, a sample of 10 batches is produced using the first catalyst and 12 using the second. If the resulting data is  EMBED Equation.2  and  EMBED Equation.2 , can we reject, at the 10% significance level, the hypothesis of equal variance? b) An ordinary 6-sided die is rolled repeatedly until the first 6 is obtained. Ole џџџџџџџџџџџџPIC  џџџџLPICT џџџџџџџџџџџџZCompObjџџџџ1Y currentpoint  П" О,Times .џ+ H +1 ( :, Symbol)m) <) m +0ЁРP/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1824 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (H) 9 261 sh 224 /Times-Roman f1 (1) 268 357 sh (0) 1594 357 sh 384 /Times-Roman f1 (:) 485 261 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (m) 689 261 sh (m) 1362 261 sh 384 /Symbol f1 (<) 1033 261 sh end MTsave restore  ПЁd=MATH15 ƒH ˆ1 ‚:„m†<„m ˆ0 џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў 1 ƒH ˆ1 ‚:„m†<„m ˆ0аЯрЁБс;џў аЯрЁБс;џў Lлt,шшThis experiment is done 100 times and  EMBED Equation.2  denotes the average number of rolls needed in the 100 experiments. Using the Central Limit Theorem, find P( EMBED Equation.2  > 6.5). [Hint. For a geometric random variable X with success probability p, E(X) = 1/p and Var(X) = (1-p)/p EMBED Equation.2 .] 5. The local Democratic Party Committee wants to determine the proportion p of PIC џџџџ7LPICT џџџџџџџџџџџџ9]CompObjџџџџKYObjInfoџџџџџџџџMаЯрЁБс;џў ]9ЁdЗxpr  Œ 9"9 ОЁР currentpoint  П" О,Times .џ+ H +1 ( :, Symbol)m) Й) m +0ЁРS/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1824 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (H) 9 261 sh 224 /Times-Roman f1 (1) 268 357 sh (0) 1605 357 sh 384 /Times-Roman f1 (:) 485 261 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (m) 689 261 sh (m) 1373 261 sh 384 /Symbol f1 (\271) 1037 261 sh end MTsave restore  ПЁd=MATH1В ƒH ˆ1 ‚:„m†Й„m ˆ0 џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў 1 ƒH ˆ1 ‚:„m†Й„m ˆ0аЯрЁБс;џў Equation Native џџџџџџџџџџџџNM_908716078 'РF€рЅаАП€рЅаАПOle џџџџџџџџџџџџPPIC џџџџQLаЯрЁБс;џў Lp,шшаЯрЁБс;џў і,ЁdЗxpr  Œ ,", ОЁР currentpoint  П" О,Times .џ+ S +1( 2, Symbol +=) .)14ЁРљ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1408 div 480 3 -1 roll exch div scale currentpoint translate 64 34PICT џџџџџџџџџџџџSіCompObjџџџџcYObjInfoџџџџџџџџeEquation Native џџџџџџџџџџџџfN translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (S) -3 318 sh 224 /Times-Roman f1 (1) 156 414 sh (2) 270 152 sh 384 ns (14) 936 318 sh 384 /Symbol f1 (=) 532 318 sh 384 /Times-Roman f1 (.) 840 318 sh end MTsave restore  ПЁd>MATH2г ƒS ˆ1  ˆ2 †=‚.ˆ1ˆ4 џаЯрЁБсўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў 2 ƒS ˆ1  ˆ2 †=‚.ˆ1ˆ4аЯрЁБс;џў _908716155џџџџџџџџ"РF€рЅаАПw>бАПOle џџџџџџџџџџџџhPIC !$џџџџiLPICT џџџџџџџџџџџџkіаЯрЁБс;џў L4„,шшаЯрЁБс;џў і-ЁdЗxpr  Œ -"- ОЁР currentpoint  П" О,Times .џ+ S +2( 2, Symbol +=) .)28ЁРљ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1440 div 480 3 -1 roll exch div scale currentpoint translate 64 34 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (S) -3 318 sh 224 /Times-Roman f1 (2) 174 414 sh (2) 306 152 sh 384 ns (28) 972 318 sh 384 /Symbol f1 (=) 568 318 sh 384 /Times-Roman f1 (.) 876 318 sh end MTsave restore  ПЁd>MATH2й ƒS ˆ2  ˆ2 †=‚.ˆ2ˆ8 џаЯрЁБсўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў 2 ƒS ˆ2  ˆ2 †=‚.ˆ2ˆ8аЯрЁБс;џў CompObj#%џџџџ{YObjInfoџџџџ&џџџџ}Equation Native џџџџџџџџџџџџ~N_908716455 .)РFw>бАПw>бАПOle џџџџџџџџџџџџ€PIC (+џџџџLPICT џџџџџџџџџџџџƒ„CompObj*,џџџџ’Ythe electorate favoring their candidate. If they want 95% confidence that their sample proportion is correct within (2 percentage points, how large a sample will be needed? ________ Suppose now a random sample of this size is surveyed and it turns out that 56% of the sample favor the Democrats. Explain briefly in your own words (i) why it is not technically correct to say that вThe probability that p lies between 54% and 58% аЯрЁБс;џў LЇЫ№шшаЯрЁБс;џў „ ЁdЗxpr  Œ "  ОЁР currentpoint  П" О,Times .џ+ X"ЁРЮ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 384 div 416 3 -1 roll exch div scale currentpoint translate 64 43 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 8 moveto 260 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (X) 17 341 sh end MTsave restore  ПЁdMATH ƒX џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў  ƒXаЯрЁБсаЯрЁБс;џў LЇЫ№шшObjInfoўџ џџџџ-џџџџџџџўўџџџ” Equation Native)*+,-./0 џџџџџџџџџџџџ5џџўџџџџў8ўџџџ•/@_908716601FGHIJџџўџLџџўџџџўџOџџўџџџџџ50РFw>бАПw>бАП^_`Oleўџdџџўџџџўџgџџўџџџўџjџџўџlmnop џџџџџџџџџџџџuvwxy–џџџўPIC /2џџџџ—LPICTbj џџџџџџџџџџџџ™ФCompObj13џџџџЉYObjInfoNativeџџџџ4џџџџЋаЯрЁБс;џў Ф џ џџџџ ЁdЗxpr  Œ "  ОЁР currentpoint  П" О,Times .џ + X"ЁРЮ/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 384 div 416 3 -1 roll exch div scale currentpoint translate 64 43 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 0 8 moveto 260 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Italic f1 (X) 17 341 sh end MTsave restore  ПЁdMATH ƒX џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў  ƒXаЯрЁБсаЯрЁБс;џў LїЫ­шшаЯрЁБс;џў Equation Native џџџџџџџџџџџџЌ/_908716739џџџџџџџџ7РFw>бАПw>бАПOle џџџџџџџџџџџџ­PIC 69џџџџЎLPICT џџџџџџџџџџџџАCompObj8:џџџџНYObjInfoџџџџ;џџџџПEquation Native џџџџџџџџџџџџР1 ЁdЗxpr  Œ "  ОЁР currentpoint  П" О,Times .џ+2ЁРm/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 224 div 416 3 -1 roll exch div scale currentpoint translate 32 60 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 224 /Times-Roman f1 (2) 26 152 sh end MTsave restore  ПЁd!MATHќ  ˆ2 џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў is .95г. (ii) the precise sense in which it is correct to say that p lies between 54% and 58% with confidence .95. PAGE  PAGE 5 ™ ІоЇ8Ја|HHк(џсџсљEG(ќHHи(d'hџџ`Ÿ`џџаЯрЁБс;џwith vertices (0,0), (1,0) and (1,2) (Thus the hypotenuse of the triangle has equation y = 2x.) 3 turned out to be .042 3џџџџџџџџџџџџџџџџџџџџџџ“ІГЛ8E#BЫкkzњ    . / 0 1 9 : M N O P N O b c d e Њ Џ Е К   !&':;<=&':ќњќњќњќњќњќњќњќњќњєњъсєњєњзЮєњєњФЛєњќњќњєњБЈєњєњž•єњєњuD{ш)6]eјџKuD{ш)6acvKuD.ш)6]eјџKuD.ш)6acvKuD„у)6]eіџKuD„у)6acvKuDМт)6]eіџKuDМт)6acvKuD_т)6]eіџKuD_т)6acvK uD]]]^6:;<=šЏИЙЬЭЮЯQRefgh‡ˆ”•›œŸ ІЇЈЉЊ­ЎUknxy|‚Ќ­ГЛМФХЦфшщъіэчхтхчхиЯчхчхХМчхЗхБЏБЏБЏБЏБЏх­ххххххххххххЏххЏuP uDPJБ]uDУъ)6]eўџKuDУъ)6acvKuD9ъ)6]eўџKuD9ъ)6acvK]^] uD]uDЇщ)6]eўџKuDЇщ)6acvK4dЋМНэю FGˆ‰‹ТУФХЦЧШЩЪЫЬЭЮЯ FGyЌ­м :;IjmnoќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'Т-oq”•–—лмнBCopЎЏАБВГДЕЖЗИЙстEFGHIJKLM“ЖНЬЭЮќФ'ќФ'ќФ'ќФ'ќФ'ќФ'їФ'їФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ТжќТ,ЮЯабвгдежзийкстуф) q Е §  S ˜ ™ м н о п р с т у ф х ц ч ш щ ъ ы ь э ю ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'Т,ю я Q u v П ч ш    o З Ц № ё і ї 9 ~ • в г д aЉђZ–—˜™š›œžŸ ЁЂќФ'ќФ',їФ'їФ'їФ'їФ'їФ'їФ'їФ'їФ'ђФ',ђФ'ђФ'ђФ'їФ'эФ'эФ'эФ'эФ'эФ'эФ'їФ'їФ'шФ'шФ'шФ'шФ'шФ',шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'Т>ўv˜ўТђўТжќ)ЂЃЄЅ№L‰Šий"klmnopqrst‰Š‹ŒŽ‘’“”•–юIЄДмћФ'ћФ'ћФ'ћФ'ћФ',ћФ'ћФ'ћФ',ћФ'ћФ'ћФ',ћФ'ћФ'ћФ'ћФ'іФ'іФ'іФ'іФ'яФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'шФ'шФ'шФ'шФ'шФ'сФ'сФ'сФ'кФ'кФ'˜ўhZ˜ўжќ|ќ˜ўТжќLџТжќТжќТ>ў'мнV]…†г     ^”žŸЊЋЌ­Ў|­ХщљФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'ђюьђюььљФ'шФ'шФ'ььТh`јџ%˜ўТжќ K@ёџNormala c.@. Heading 1 №< U]ck"A@ђџЁ"Default Paragraph Font @ђ Footer рР!)@Ђ Page Number ЎЛ!џџ џџ џџ џџ џџмB3 ѕ DpИїАН Ф'Ф'Ф'Ф' :ъ oЮю Ђмщ y˜ЌЎ­ С У i }  … ™ › … ™ › +-АФЦ :”џ•€:”џ•€:”џ•„:”џ•€:”џ•€:”џ•€:”џ•€:”џ•€ !•!џ•€ ѓUniversity of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin+Power Mac 7200:Desktop Folder:Nov_99_Test_2University of Wisconsin2Power Mac 7200:Desktop Folder:test 2:Nov_99_Test_2University of WisconsinCMacintosh HD:Files:David's Files:public:html:stat_224:Nov_99_Test_2џ@€ЮЮЮА јHЅЈВГЕИОЬії§АЮвђѓў   Uknxy|Ÿ‚Ќ­ГЛМ­ЖЦфs ш”ŸщЈЋ­[MTimes New Roman Symbol MArial MCourier MTimesMHelvetica"1ˆаhHD&YU{&ƒ!‚@1. a) Using the axes below draw a box plot to represent the dataUniversity of WisconsinUnEquation Native џџџџџџџџџџџџЌ/_908716739џџџџџџџџ7РFw>бАПw>бАПOle џџџџџџџџџџџџ­PIC 69џџџџЎLObjInfoўџ џџџџ-џџџџџџџўўџџџ” Equation Native)*+,-./0 џџџџџџџџџџџџ5џџўџџџџў8ўџџџ•/@_908716601FGHIJџџўџLџџўџџџўџOџџўџџџџџ50РFw>бАПw>бАП^_`Oleўџdџџўџџџўџgџџўџџџўџjџџўџlmnop џџџџџџџџџџџџuvwxy–џџџўRџџџџџџџџ РF€эЎH'žП€2CompObjџџџџџџџџџџџџ\WordDocumentџџџџ<џџџџJп-ObjectPool€рЅаАПw>бАПџџџџџџџџGџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџaџџџџ "!#&$%)',џџџџ*+.-1/032F4Iџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџc§џџџўџџџўџџџўџџџHKLMNOPQRSTUVWXYZ[\]^_`ўџџџbџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџSummaryInformation (џџџџџџџџџџџџџџџўўџџџС  Equation Native)*+,-./0џџџџџџџџџџџџ5џџўџџџџў8ўџџџ•/@_908716601FGHIJџџўџLџџўџџџўџOџџўџџџџџџџџџџџџџРFw>бАПw>бАП^_`Oleўџdџџўџџџўџgџџўџџџўџjџџўџlmnopџџџџџџџџџџџџuvwxy–џџџўўџџџ‚ўџџџ„…†‡ˆ‰Š‹ŒŽ‘ўџџџ“ўџџџўџџџўџџџўџџџ˜ўџџџš›œžŸ ЁЂЃЄЅІЇЈўџџџЊўџџџўџџџўџџџўџџџЏўџџџБВГДЕЖЗИЙКЛМўџџџОўџџџўџџџўџџџТУФХЦЧШЩўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ@Microsoft Word 6.0.13аЯрЁБс;џў џџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ  ˆ2аЯрЁБсўџ ђŸ…рOљhЋ‘+'Гй0н˜з @` f r ~Š’ šІУ ЫеFFFFFFFFFF FFFFFFFFFFFFF7Power Mac 7200:Applications:Microsoft:Templates:NormalA1. a) Using the axes below draw a box plot to represent the dataUniversity of WisconsinUniversity of Wisconsin'@ИБАП@€vгђЬч@˜ц''žПмЅhSР eЎп-ѓ&ж&жж&ж&ж&ж&ж&v'@'6v'v'v'†'–'(v'Њ,[О'”R("t(t(t(x(x(x(Y+[+[+[+[+[+[+&-X]-‚+)ж&x( t(x(x(x(+x(ж&ж&t(О'x(x(x(x(ж&t(ж&t(Y+ъ& '6ж&ж&ж&ж&x(Y+x(сx(Sample Test 2 for Stat. 224 1. a) Using the following 10 random digit pairs, simulate 10 values of the discrete random variable X with probability density function X = 0 1 2 3 prob. = .12 .12 .60 .16 Random Digits 1 6 8 7 1 6 5 5 4 9 6 0 1 4 1 9 9 2 5 2 How many 2's in your list of simulated values? _______ b) Three independent normal random variables X,Y,Z have respective mean and standard deviation as follows random standard variable mean deviation X 2.0 0.8 Y 1.2 0.2 Z 1.6 0.4 Find (i) E(3X - 2Y + Z) (ii) Var(3X - 2Y + Z) What distribution does the random variable 3X - 2Y + Z have? 2. a) A pair of continuous random variables X,Y have the joint probability density function f(x,y) = 3/4 (x+y) on the triangular region sketched below, = 0 elsewhere. Fill in the marginal p.d.f. for X f(x) = 0 x < 0 or x > 1 = ___________ 0 < x < 1 b) The probability that a standard normal random variable Z lies between a and -a is .8664. Find a. 3. a) The manufacturer of a new fiberglass tire claims that they will last longer than the old tires which had an average life of 40,000 miles. To check this claim, a sample of 12 tires is tested with their lifetimes (in 1000еs of miles) being as follows Tire 1 2 3 4 5 6 7 8 9 10 11 12 Life 38.1 40.2 42.8 36.5 42 39.8 42 41 44.8 37.2 43 41 Test the manufacturerеs claim at the 5% significance level. b) The P-value for the hypothesis test  EMBED Equation.2  versus  EMBED Equation.2  turned out to be .416. (i) Would you reject the null hypothesis at the the 5% significance level? YES NO (Circle one) (ii) If the alternative hypothesis was  EMBED Equation.2  and the exact same sample data were obtained, what would the P-value be now? _________ (iii) If you were trying to persuade your boss that the alternative hypothesis was true, would you prefer a large or small P-value? (Circle one) 4. a) There are two different choices of a catalyst to stimulate a chemical process.To test whether the variance of the yield is the same no matter which catalyst is used, a sample of 10 batches is produced using the first catalyst and 12 using the second. If the resulting data is  EMBED Equation.2  and  EMBED Equation.2 , can we reject, at the 10% significance level, the hypothesis of equal variance? b) An ordinary 6-sided die is rolled repeatedly until the first 6 is obtained. This experiment is done 100 times and  EMBED Equation.2  denotes the average number of rolls needed in the 100 experiments. Using the Central Limit Theorem, find P( EMBED Equation.2  > 6.5). [Hint. For a geometric random variable X with success probability p, E(X) = 1/p and Var(X) = (1-p)/p EMBED Equation.2 .] 5. The local Democratic Party Committee wants to determine the proportion p of the electorate favoring their candidate. If they want 95% confidence that their sample proportion is correct within (2 percentage points, how large a sample will be needed? ________ Suppose now a random sample of this size is surveyed and it turns out that 56% of the sample favor the Democrats. Explain briefly in your own words (i) why it is not technically correct to say that вThe probability that p lies between 54% and 58% is .95г. (ii) the precise sense in which it is correct to say that p lies between 54% and 58% with confidence .95. PAGE  PAGE 5 ™ ІоЇ8Ја|HHк(џсџсљEG(ќHHи(d'hџџ`Ÿ`џџаЯрЁБс;џwith vertices (0,0), (1,0) and (1,2) (Thus the hypotenuse of the triangle has equation y = 2x.) 3џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ“ІГЛ8E#BЫкkzњ    . / 0 1 9 : M N O P N O b c d e Њ Џ Е К   !&':;<=&':ќњќњќњќњќњќњќњќњќњєњъсєњєњзЮєњєњФЛєњќњќњєњБЈєњєњž•єњєњuD{ш)6]eјџKuD{ш)6acvKuD.ш)6]eјџKuD.ш)6acvKuD„у)6]eіџKuD„у)6acvKuDМт)6]eіџKuDМт)6acvKuD_т)6]eіџKuD_т)6acvK uD]]]^6:;<=šЏИЙЬЭЮЯQRefgh‡ˆ”•›œŸ ІЇЈЉЊ­ЎUknxy|‚Ќ­ГЛМФХЦіэчхтхчхиЯчхчхХМчхЗхБЏБЏБЏБЏБЏх­ххххххххххххЏuP uDPJБ]uDУъ)6]eўџKuDУъ)6acvKuD9ъ)6]eўџKuD9ъ)6acvK]^] uD]uDЇщ)6]eўџKuDЇщ)6acvK0dЋМНэю FGˆ‰‹ТУФХЦЧШЩЪЫЬЭЮЯ FGyЌ­м :;IjmnoќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'Т-oq”•–—лмнBCopЎЏАБВГДЕЖЗИЙстEFGHIJKLM“ЖНЬЭЮќФ'ќФ'ќФ'ќФ'ќФ'ќФ'їФ'їФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ТжќТ,ЮЯабвгдежзийкстуф) q Е §  S ˜ ™ м н о п р с т у ф х ц ч ш щ ъ ы ь э ю ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'ќФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'јФ'Т,ю я Q u v П ч ш    o З Ц № ё і ї 9 ~ • в г д aЉђZ–—˜™š›œžŸ ЁЂќФ'ќФ',їФ'їФ'їФ'їФ'їФ'їФ'їФ'їФ'ђФ',ђФ'ђФ'ђФ'їФ'эФ'эФ'эФ'эФ'эФ'эФ'їФ'їФ'шФ'шФ'шФ'шФ'шФ',шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'шФ'Т>ўv˜ўТђўТжќ)ЂЃЄЅ№L‰Šий"klmnopqrst‰Š‹ŒŽ‘’“”•–юIЄДмћФ'ћФ'ћФ'ћФ'ћФ',ћФ'ћФ'ћФ',ћФ'ћФ'ћФ',ћФ'ћФ'ћФ'ћФ'іФ'іФ'іФ'іФ'яФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'іФ'шФ'шФ'шФ'шФ'шФ'сФ'сФ'сФ'кФ'кФ'˜ўhZ˜ўжќ|ќ˜ўТжќLџТжќТжќТ>ў'мнV]…†г     ^”žŸЊЋЌ­Ў|­ХљФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'љФ'ђюьђюььљФ'шФ'шФ'ьТh`јџ%˜ўТжќK@ёџNormala c.@. Heading 1 №< U]ck"A@ђџЁ"Default Paragraph Font @ђ Footer рР!)@Ђ Page Number ЎЛ!џџ џџ џџ џџ џџмB3 ѕ DpИїН Ф'Ф'Ф'Ф' :Ц oЮю ЂмХ y˜ЌЎ­ С У i }  … ™ › … ™ › +-АФЦ :”џ•€:”џ•€:”џ•„:”џ•€:”џ•€:”џ•€:”џ•€:”џ•€ !•!џ•€ сUniversity of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin1Power Mac 7200:Temporary Items:Word Work File A 5University of Wisconsin+Power Mac 7200:Desktop Folder:Nov_99_Test_2University of Wisconsin2Power Mac 7200:Desktop Folder:test 2:Nov_99_Test_2џ@€ ј$ЅЈВГЕИОЬії§ђѓў   Uknxy|Ÿ‚Ќ­ГЛМ­ЖФ”ŸХЈЋ­[MTimes New Roman Symbol MArial MCourier MTimesMHelvetica"1ˆаhHD&а"DFƒ!‚@1. a) Using the axes below draw a box plot to represent the dataUniversity of WisconsinUniversity of Wisconsinў†ObjInfoџџџџџџџџ3Equation Native џџџџџџџџџџџџ4M_908714884џџџџџџџџРF€рЅаАП€рЅаАПOle џџџџџџџџџџџџ6CompObj џџџџYObjInfoџџџџ џџџџEquation Native џџџџџџџџџџџџM_908714684 РF€рЅаАП€рЅаАП_908714591џџџџџџџџРF€рЅаАП€рЅаАПOle џџџџџџџџџџџџPIC џџџџLPICT џџџџџџџџџџџџZCompObj#%џџџџ{YObjInfoџџџџ&џџџџ}Equation Native џџџџџџџџџџџџ~N_908716455 .)РFw>бАПw>бАП_908716155џџџџџџџџ"РF€рЅаАПw>бАПOle џџџџџџџџџџџџhPIC !$џџџџiLPICT џџџџџџџџџџџџkіEquation Native џџџџџџџџџџџџNM_908716078 'РF€рЅаАП€рЅаАПOle џџџџџџџџџџџџPPIC џџџџQLObjInfoџџџџџџџџ3Equation Native џџџџџџџџџџџџ4M_908714884џџџџџџџџРF€рЅаАП€рЅаАПOle џџџџџџџџџџџџ6CompObj џџџџYObjInfoџџџџ џџџџEquation Native џџџџџџџџџџџџM_908714684 РF€рЅаАП€рЅаАП_908714591џџџџџџџџРF€рЅаАП€рЅаАПOle џџџџџџџџџџџџPIC џџџџLPICT џџџџџџџџџџџџZ